
The projection operator \(P_r(\cdot )\)  [1]} is defined as in Section .
Infinitesimal motions, therefore, are motions \(x(t)\)  produced by velocities \(v(t)\)  that lie in the nullspace of \(\mathcal {R}_\mathcal {G}\) , for which it holds that \(\dot{\gamma }_\mathcal {G} = \mathcal {R}_\mathcal {G}(x(t)) v(t) = 0\) , where \(v[\dot{p}_1^\top ,\omega _1^\top ,\dots ,\dot{p}_N^\top ,\omega _N^\top ]^\top \) , as defined in Section . The infinitesimal motions therefore depend on the number of motion degrees of freedom the entire framework possesses. This directly relates to the structure of the underlying graph. 
Motions that preserve the distances and bearings of the framework for any underlying graph are called \(D\& B\)  trivial motions. This leads to the definition of infinitesimal rigidity.
